Nonmagnetic Ground State of Rutile RuO$_2$ from Diffusion Quantum Monte Carlo

Abstract

Rutile RuO$_2$ has been proposed as an altermagnet, but its bulk magnetic ground state is still under debate because density-functional calculations give conflicting predictions. Using fixed-node diffusion quantum Monte Carlo, we find that stoichiometric bulk RuO$_2$ is nonmagnetic in the pristine structure, lying 23(9) meV per formula unit below the lowest antiferromagnetic state considered. A 3$\%$ compressive strain instead stabilizes antiferromagnetism, placing RuO$_2$ near a strain-tunable magnetic instability and helping reconcile apparently conflicting experimental reports.

Figures (4)

• Figure 1: (a) Crystal structure of rutile RuO$_2$ (RuO$_6$ octahedra). (b) DFT magnetic ordering energy $E_{\mathrm{AFM}}-E_{\mathrm{NM}}$ versus Ru local moment across representative functionals; dotted line is a guide to the eye.
• Figure 2: (a) Twist-averaged fixed-node DMC energies for NM and AFM states using PBE0($\omega$) trial nodes. (b) DMC magnetic ordering energy $E_{\mathrm{AFM}}-E_{\mathrm{NM}}$ versus Ru local moment estimated with DMC using PBE0($\omega$) and PBE+$U$. Stars denote the variationally optimal point within each functional class, representing the best value of the exact-exchange fraction $\omega$ for PBE0 and the optimal Hubbard $U$ parameter for the PBE+$U$ functionals.
• Figure 3: (a) Fixed-node DMC $E_{\mathrm{AFM}}-E_{\mathrm{NM}}$ under $\pm 3\%$$z$ strain using PBE0($\omega$) trial nodes. (b) Ru local moment versus $\omega$ for strained RuO$_2$. Stars denote the variationally optimal exact-exchange fraction $\omega$ of PBE0 for each applied strain case.
• Figure 4: (a) Isosurfaces of spin density distribution for AFM phase obtained from DMC based on PBE0 orbitals with $\omega = 0.20$. The isosurface levels are $\pm 2 \times 10^{-5}$ with the spin-up and spin-down electrons being represented by yellow and blue colors, respectively. (b) Isosurface of the DMC charge-density difference between calculations based on PBE0 orbitals with $\omega=0.20$ and $\omega=0.10$. Yellow indicates regions where the DMC charge density is higher for $\omega=0.20$ than for $\omega=0.10$, while blue indicates regions where it is lower. The isosurface levels are $\pm 3\times 10^{-6}$.